Solitaire is a family of well-known single-player card games which are generally similar in character, but vary in detail. One widely known solitaire game is Klondike, sometimes referred to herein as “Klondike Solitaire.”
Klondike Solitaire utilizes a conventional deck of 52 playing cards. To begin a play of a game of Klondike Solitaire, 28 cards of the 52 card deck are dealt into seven piles. Each pile occupies a position. The first pile includes one card, the second pile includes two cards, and so on up to seven cards in the seventh pile. The top card of each pile is dealt face up and the other cards in each pile are dealt face down. The space the piles occupy is sometimes referred to as the “field.”
The remaining 22 cards of the 52 card deck, which were not dealt into the initial seven piles, are referred to as stock cards. The stock cards are left face-down in a stock pile. The stock cards are turned up from the stock pile sequentially during game play. In certain versions of Klondike Solitaire, the stock cards are turned face up one at a time. In other versions, the stock cards are turned face up three at a time (i.e., every third card is turned face up). In some versions of Klondike Solitaire, the player may run through the stock cards one time during a play of the game. In other versions, the player may run through the stock cards multiple times during a play of the game.
Klondike Solitaire also includes four banks positioned above the seven piles. Klondike Solitaire includes one bank for each suit of cards (i.e., one for each of diamonds, hearts, spades and clubs). When the cards are initially dealt, these four banks or positions do not have any cards in them. Cards can only be placed in each respective bank or position in order (i.e., ace, two, three . . . King).
The ultimate objective of Klondike Solitaire is to accumulate all 52 cards of the deck into the respective banks. Cards must be accumulated in each respective bank in-suit and in ascending sequence (i.e., ace to king of the respective suit). A player completes or solves the Klondike Solitaire game when each bank includes all 13 cards of its respective suit. Placing a card in a bank or causing a card to be placed in a bank is sometimes referred to as “banking” a card. To accomplish this objective, a player may move or cause the movement of the cards according to a designated set of governing rules which are generally explained below.
The movement of the cards are governed by specific rules. When the stock cards are turned face up (as discussed below), they are placed in a discard pile, placed in the field or placed in one or more of the banks. A player may move cards from the stock pile, the discard pile and the field into the banks according to these rules, after they are turned up. Once turned up, the stock cards may also be moved to the field or the discard pile, according to these rules. Cards from the discard pile may be moved to the field or placed into a bank. A player may move face-up cards in any of the piles in the field either to another pile in the field or into a bank. A series of rules also govern the arrangement of cards in the field.
More specifically, a player may associate a number of cards with the face-up card on the top of each pile by “building” cards into a column. In Klondike Solitaire, cards must be built in descending sequence and alternating in color (i.e., red from black or black from red). For example, if the king of spades is face up on the top of a pile, a player may build a queen of hearts or a queen of diamonds onto the king of spades.
A player may move a face-up card from one pile or column to another pile or column, within these guidelines. Multiple face-up cards from one column may be built onto another pile or column as a unit. For example, if a column includes a seven of clubs and an eight of diamonds, a player may move these two cards together and build them onto a nine of spades or nine of clubs on another pile or at the bottom of another column.
When the player uncovers a face-down card on a pile, that card may be turned face up. The player is always entitled to seven piles. Thus, if no cards remain in the position of a pile, the player may put a king in that pile or position to start the pile.
A card may not be placed in a bank from the field unless it is “free.” Cards which are free include cards which are face-up and either not associated with any other cards or the lowest card in a column. For example, if a built column includes a king of spades, a queen of hearts and a jack of spades, and a ten of spades is already in the bank associated with spades, then the jack of spades is “free” and may be moved into its respective bank.
Klondike Solitaire is a very popular game and is probably one of the best-known and most played solitaire games in the world. This game is played with conventional decks by hand by millions of people and played on millions of personal computers, handheld communication devices and other electronic devices worldwide.
While simple to play (i.e., moving cards subject to the governing rules), Klondike Solitaire is extremely complicated. Some estimates are that there are billions of possible different ways that a Klondike Solitaire game can be played with a standard 52 card deck based on the order of the cards and the movements of the cards by the player. Despite the vast popularity of this game, the exact proportion of Klondike games that will be won is currently unknown because no mathematical model known to the inventors is simple enough to allow direct computation of such exact probability or probabilities. No consensus also exists as to the probabilities associated with various non-winning game outcomes for each play of the game (i.e., the probability associated with having each of a number of less than 52 cards banked at the end of a game or before a player can not make any further moves of the cards). Similarly, formulas for determining such probabilities within suitable determinable margins of error or limited tolerances are not known. This is because of the amount of variables. Casino or gambling games typically require all of the exact probabilities or probabilities within limited tolerances of winning a game to be known, calculated and verifiable. For example, three wheel slot games typically have the exact probabilities worked out. Because the probabilities of Klondike Solitaire games are not known or calculated (within suitable tolerances) even with intense study, Klondike Solitaire has not been made into a suitable casino or wagering game.
Moreover, while such probabilities are not exactly known or known within suitable determinable margins of error or limited tolerances, it is somewhat known that people solve or complete the game about one in forty-five plays. Thus, another problem with making Klondike Solitaire a casino game is that a relatively big award can not be associated with solving the game because it happens too often.
More specifically, to create a suitable Klondike Solitaire wagering game, one would have to create a suitable paytable. Paytables are typically created to achieve a suitable designated average expected payback percentage and thereby be verifiable and approvable by gaming regulatory agencies. The average expected payback percentage of a paytable is a function of the respective exact probabilities or probabilities within limited tolerances of the player achieving each and every of the outcomes in the paytable and the respective awards associated with those outcomes.
Thus, to create a suitable paytable for a Klondike Solitaire game, one would need to know the exact probabilities of or have verifiable probabilities with limited tolerances associated with each of the various outcomes or events one seeks to include in the paytable. Absent these exact or verifiable probabilities (with limited tolerances), awards associated with those outcomes are difficult, if not impossible, to calculate such that the paytable achieves a suitable designated average expected payback percentage.
It is noted that in some land-based and online casinos, Las Vegas Solitaire is played. Las Vegas Solitaire is similar to Klondike Solitaire. In Las Vegas Solitaire, the player turns over stock cards one at a time, and is only allowed to go through the stock pile once. The player is provided with an award for each card successfully banked. In one known version, it costs the player 52 credits to play a game. The game pays 5 credits for each card banked. To break even, the player needs to bank 10 cards before going through the stock pile one complete time. The players are awarded as play progresses by the cards banked.
Accordingly, a need exists for (a) a method for determining the suitable probabilities within acceptable tolerances associated with the various Klondike Solitaire outcomes based on various strategies and rules of play; and (b) at least one paytable based on these probabilities which achieves a suitable designated average expected payback percentage.
Also, a need exists for a gaming device including a suitable wagering Klondike Solitaire game associated with such a paytable.